derivative y=(x^2+x+1)^{100}

Lösung

ableitung von

y = (x^{2} + x + 1)^{100}

100 (x^{2} + x + 1)^{99} (2 x + 1)

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + x + 1)^{100})

Wende die Kettenregel an:

100 (x^{2} + x + 1)^{99} \frac{d}{d x} (x^{2} + x + 1)

= 100 (x^{2} + x + 1)^{99} \frac{d}{d x} (x^{2} + x + 1)

\frac{d}{d x} (x^{2} + x + 1) = 2 x + 1

= 100 (x^{2} + x + 1)^{99} (2 x + 1)

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